# What is the equation of the line passing through (13,7) and (4,2)?

Nov 11, 2015

Use the two coordinate equation and rearrange into the form #y=mx+c

#### Explanation:

The Two Coordinate Equation
The general form of the two coordinate equation is $\frac{y - {y}_{1}}{{y}_{2} - {y}_{1}} = \frac{x - {x}_{1}}{{x}_{2} - {x}_{1}}$ when you have the coordinates $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$.

In your example ${x}_{1} = 13$, ${x}_{2} = 4$, ${y}_{1} = 7$ and ${y}_{2} = 2$

Putting these values into the equation we get: $\frac{y - 7}{2 - 7} = \frac{x - 13}{4 - 13}$

Next we can simplify it by cleaning up the denominators of both fractions to get: $\frac{y - 7}{-} 5 = \frac{x - 13}{-} 9$

Rearranging into the form $y = m x + c$

To rearrange into this form we must first get rid of the fractions. To get rid of the first fraction we can multiply both sides by -5.

Doing this gives us $y - 7 = \frac{- 5 x + 65}{-} 9$

To get rid of the second fraction we can multiply both sides by -9 to give us: $- 9 y + 63 = - 5 x + 65$

Next we can take away 63 from both sides to get y on its own: $- 9 y = - 5 x + 2$

Next we can divide by 9 to get $- y$: $- y = - \frac{5}{9} x + \frac{2}{9}$

Finally we multiply by -1 to flip the signs: $y = \frac{5}{9} x - \frac{2}{9}$